Please respond to as many of the following prompts as you can by writing readable and valid arguments that exhibit mathematical fluency to the extent that you can do this. 1. Recall that we discussed number systems by writing an ordered triple (X, Y, Z), where X is a set of things we call `numbers', Y is the notation for an operation we call `addition', and Z is a notation for what we call `multiplication'. We can do something analogous with Logical Systems: we specify the set of statements, the function that determines truth, and the logical operations and operators. For the logical system that we (and essentially everyone) use, let's use the notation (M, Φ, =⇒ , ∧, ∨,¬) to mean that M is the set of statements we work with, Φ is the function that assesses truth, and the others are the logical operations and operator. Please prove or disprove that the our logical system (M, Φ, =⇒ , ∧, ∨,¬) can be replaced with (M, Φ, ∇), where ∇ is dened as follows. For x, y ∈ M, x ∇ y is equivalent to ¬(x ∨ y).
2. Prove that the following game must have a winner. Place 6 dots equally spaced on a circle on a piece of paper. Player A has a red marker and Player B has a blue marker. Players take turns connecting pairs of dots with line segments using their respective colored markers, only one line segment between any two dots (therefore at most 15 line segments will be drawn). The winner is the rst to connect three dots mutually with their respective color, that is, the rst to create a monochromatic \triangle" in their marker's color.
3. Diagram the argument you gave above, using only logical operations and variables such as S1, S2, . . . for the statements made
Please respond to as many of the following prompts as you can by writing readable and...
Please respond to as many of the following prompts as you can by writing readable and valid arguments that exhibit mathematical fluency to the extent that you can do this. please show work clearly and show which answer is for what question. You do not need to answer the second question, I just have it to clear what the third question is about 1. Recall that we discussed number systems by writing an ordered triple (X, Y, Z), where X...
can you please prove the following theorem using the provided
axioms and defintions. using terms like suppose in a paragraph
format. please write clearly or type if you can !
1 Order Properties Undefined Terms: The word "point and the expression "the point z precedes the point y will not be defined. This undefined expression wil be written z < y. Its negation, "z does not precede y," will be written y. There is a set of all points, called...
Please prove the following
theorems using the provided axioms and definitions, using terms
like suppose, let..ect. Please WRITE CLEARLY AND TYPE IF YOU
CAN.
1 Order Properties Undefined Terms: The word "point" and the expression "the point x precedes the point y" will not be defined. This undefined expression will be written x 〈 y. Its negation, "x does not precede y," will be written X y. There is a set of all points, called the universal set, which is...
Can someone please help me with this code? I'm writing in C++. Thank you in advance. Complete a program that represents a Magic Eight Ball (a Magic Eight Ball allows you to ask questions and receive one of several random answers). In order to complete this, you will need a couple of new functions. First, in order to get a line of input that can contain spaces, you cannot use cin, but instead will use getline: string question; cout <<...
please help me with the ones you can. thank you!!
Solve for x in the equation: In = 10 1.3x10-4 Report your answer with 2 significant figures. A/ Question 2 (1 point) The decomposition of hydrogen peroxide is described below. 2 H2O2 (aq) → → 2 H2O (1) +O2 (g) rate = k[H202] The rate constant for the reaction is 5.3x10-4 M/s. If the initial concentration of hydrogen peroxide is 0.320 M, calculate the time it takes for the concentration...
Game Description: Most of you have played a very interesting game “Snake” on your old Nokia phones (Black & White). Now it is your time to create it with more interesting colors and features. When the game is started a snake is controlled by up, down, left and right keys to eat food which appears on random locations. By eating food snake’s length increases one unit and player’s score increases by 5 points. Food disappears after 15 seconds and appears...
could you please help me with this problem, also I
need a little text so I can understand how you solved the
problem?
import java.io.File; import java.util.Scanner; /** *
This program lists the files in a directory specified by * the
user. The user is asked to type in a directory name. * If the name
entered by the user is not a directory, a * message is printed and
the program ends. */ public class DirectoryList { public static...
Assignment Overview In Part 1 of this assignment, you will write a main program and several classes to create and print a small database of baseball player data. The assignment has been split into two parts to encourage you to code your program in an incremental fashion, a technique that will be increasingly important as the semester goes on. Purpose This assignment reviews object-oriented programming concepts such as classes, methods, constructors, accessor methods, and access modifiers. It makes use of...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
For your Project, you will develop a simple battleship game. Battleship is a guessing game for two players. It is played on four grids. Two grids (one for each player) are used to mark each players' fleets of ships (including battleships). The locations of the fleet (these first two grids) are concealed from the other player so that they do not know the locations of the opponent’s ships. Players alternate turns by ‘firing torpedoes’ at the other player's ships. The...